Compared with the SN observation, the GW observation can have a larger number of samples, smaller systematic errors, and higher redshifts in the future. According to the design and objectives of DECIGO [1]}, the detectable number of GW events from BNS merger could reach \(10^5\)  per year within a redshift of 5. Moreover, since the signals can be observed several years before the merge, the accuracies of the direction of GW source and the predicted coalescence time could be greatly improved, making the tracking of its electromagnetic counterpart more reliable. Therefore, in the GW multi-messenger astronomy era, we can use this method to measure \(H(z)\) , and then to explore the nature of dark energy.
